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A novel robust principal component analysis method for image and video processing

Guoqiang Huan, Ying Li, Zhanjie Song (2016)

Applications of Mathematics

The research on the robust principal component analysis has been attracting much attention recently. Generally, the model assumes sparse noise and characterizes the error term by the ℓ 1 -norm. However, the sparse noise has clustering effect in practice so using a certain ℓ p -norm simply is not appropriate for modeling. In this paper, we propose a novel method based on sparse Bayesian learning principles and Markov random fields. The method is proved to be very effective for low-rank matrix recovery...

A one-way ANOVA test for functional data with graphical interpretation

Tomáš Mrkvička, Mari Myllymäki, Milan Jílek, Ute Hahn (2020)

Kybernetika

A new functional ANOVA test, with a graphical interpretation of the result, is presented. The test is an extension of the global envelope test introduced by Myllymäki et al. (2017, Global envelope tests for spatial processes, J. R. Statist. Soc. B 79, 381-404, doi: 10.1111/rssb.12172). The graphical interpretation is realized by a global envelope which is drawn jointly for all samples of functions. If a mean function computed from the empirical data is out of the given envelope, the null hypothesis...

A posteriori disclosure risk measure for tabular data based on conditional entropy.

Anna Oganian, Josep Domingo-Ferrer (2003)

SORT

Statistical database protection, also known as Statistical Disclosure Control (SDC), is a part of information security which tries to prevent published statistical information (tables, individual records) from disclosing the contribution of specific respondents. This paper deals with the assessment of the disclosure risk associated to the release of tabular data. So-called sensitivity rules are currently being used to measure the disclosure risk for tables. This rules operate on an a priori basis:...

A practical application of kernel-based fuzzy discriminant analysis

Jian-Qiang Gao, Li-Ya Fan, Li Li, Li-Zhong Xu (2013)

International Journal of Applied Mathematics and Computer Science

A novel method for feature extraction and recognition called Kernel Fuzzy Discriminant Analysis (KFDA) is proposed in this paper to deal with recognition problems, e.g., for images. The KFDA method is obtained by combining the advantages of fuzzy methods and a kernel trick. Based on the orthogonal-triangular decomposition of a matrix and Singular Value Decomposition (SVD), two different variants, KFDA/QR and KFDA/SVD, of KFDA are obtained. In the proposed method, the membership degree is incorporated...

A probability density function estimation using F-transform

Michal Holčapek, Tomaš Tichý (2010)

Kybernetika

The aim of this paper is to propose a new approach to probability density function (PDF) estimation which is based on the fuzzy transform (F-transform) introduced by Perfilieva in [10]. Firstly, a smoothing filter based on the combination of the discrete direct and continuous inverse F-transform is introduced and some of the basic properties are investigated. Next, an alternative approach to PDF estimation based on the proposed smoothing filter is established and compared with the most used method...

A procedure for ε-comparison of means of two normal distributions

Stanisław Jaworski, Wojciech Zieliński (2004)

Applicationes Mathematicae

For two normal distributions N(μ₁,σ²) and N(μ₂,σ²) the problem is to decide whether |μ₁-μ₂|≤ ε for a given ε. Two decision rules are given: maximin and bayesian for σ² known and unknown.

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